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Wednesday, August 20, 2014

Time reversal symmetry Breaking in Turbulence.

In three-dimensional turbulent flows, the flux of energy from large to small scales breaks time symmetry. We show here that this irreversibility can be quantified by following the relative motion of several Lagrangian tracers. We find by analytical calculation, numerical analysis, and experimental observation that the existence of the energy flux implies that, at short times, two particles separate temporally slower forwards than backwards, and the difference between forward and backward dispersion grows as t3. We also find the geometric deformation of material volumes, defined by four points spanning an initially regular tetrahedron, to show sensitivity to the time reversal with an effect growing linearly in t. We associate this with the structure of the strain rate in the flow.

One hallmark of fluid turbulence is the cascade of energy from large-scale fluid motions to smaller flow structures: they are dissipated by viscosity.

Researchers have developed various statistical models in which time asymmetry is predicted to be related to an asymmetry in the microscopic motion of particles: The expression for the distance between two particles involves an odd order term in time (t^3) which breaks symmetry. But no direct experimental probes could back up this conclusion till now...

Because in a paper in Physical Review Letters, a group in the laboratory of Eberhard Bodenschatz at the Max Planck Institute for Dynamics and Self-Organization, Germany, report a controlled laboratory study of particle movements in a turbulent flow. The researchers use a water tank with rotating blades at the top and bottom that create a turbulent fluid section, and they track the motion of suspended polystyrene microspheres with high-speed cameras.

The setup allowed the researchers to track the separation of pairs of particles as a function of time. For short times, the results confirm that the time asymmetry in pair separation depends on a t^3 term: two particles separate more slowly in the forward than in the backward direction, a clear manifestation of the breaking of time symmetry. But the authors see a stronger, linear dependence of time asymmetry when they look at how groups of four particles deform in the flow. This allows them to connect the irreversibility to a fundamental property—the rate of strain of the fluid—and suggests that multiparticle tracking might be a powerful way t study turbulence.

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